A note on the matrix equation A' LA-L = -K

Matrices W
i
and
N_{i},
which result from application of Krylov's algorithm to the matrices
A
and
B
related by
A = (B + I)(B - I)^{-1},
are shown to be row equivalent, i.e.,
N_{i} = M_{i}W_{1}
. This result is applied to solution of the Lyapunov matrix equation for discrete-time systems,
A'LA - L = -K
.